Device for coupling between free space and an electron stream



2 Sheets-Sheet l /NI/ENTOR L. R. WAL/(ER J M1715 ATTORNEY L. R. WALKERDEVICE FOR COUPLING BETWEEN FREE SPACE AND AN ELECTRON STREAM May 15,1956 Filed March 25, 1952 May 15, 1956 R. WALKER 2,746,036

DEVICE FOR COUPLING BETWEEN FREE SPACE AND AN ELECTRON STREAM FiledMarch 25, 1952 2 Sheets-Sheet 2 44 ELECTRON FLOW4/ /A/l/E/v TOR L. R.WALKER BV W A 7' TOR/VE V United States Patent DEVICE FOR COUPLINGBETWEEN FREE SPACE AND AN ELECTRON STREAM Laurence R. Walker, New York,N. Y., assigner to Bell Telephone Laboratories, incorporated, New York,N. Y., a corporation of New York Application March 2s, 1952, serial No.278,322 1s Claims. (Cl. 343-100) This invention relates to microwaveapparatus. ln a particular aspect, the invention relates to couplingarrangements for energy transfers between electron streams on which aretraveling space charge waves, as alternating current modulationcomponents, at' the velocity of the electron stream and wavetransmission circuits in which electromagnetic waves are propagating atapproximately the velocity of light.

There has been developed in recent years a number of space chargedevices which utilize for amplification the growth of space charge wavesin an electron stream. 'In these devices, velocity modulations areapplied to the electron stream by input signal waves and the excitationis propagated along the stream as space charge waves. Various expedentsare thereafter employed for the amplification of these space chargewaves, as for example, the use of electron streams with distributed ordifferent velocities. Y

In such space charge devices, it is important to secure over thefrequency range of operation eicient coupling between the electronstream and the signal input and output wave members which are coupledthereto for exciting initially thel space charge waves and abstractingthe ampliedoutput waves, respectively. Such devices generally involveconversions between waves traveling on the electron stream at electronstream velocities and waves traveling in wave transmission members atsubstantially the free space wave velocity which generally isappreciably faster than the electron stream velocities. For example, itis common to employ, as the input and output wave transmission elements,wave guides which are continuations of a wave transmission system andthrough which electromagnetic waves propagate at velocities comparableto the velocity of light. In such cases, it becomes necessary tointroduce transducers for energy exchanges between the electron streamsand the wave guides.

Various arrangements have been utilized hitherto for effecting thesedesired energy transfers. Generally, these have involved elements whichare critical in geometry and positioning. Typical are the helix typetransducers Vwhich involve wire conductors wound helically at apredetermined pitch with dimensions related to the operating frequencyrange. Such transducers do not lend themselves to ellicient large scalefabrication and assembly, particularly at the higher radio frequencies.

Accordingly, one object of this invention is to provide microwavetransducers for such energy transfers which can be made and assembledconveniently and withun'iformity.

In a microwave transducer in accordance with the invention, a wallsurface of a wave transmission member, through which are propagatingelectromagnetic waves, is slotted in a direction transverse to thecurrent flow induced in the wall surface by the propagation of wavesthrough the transmission member. Spaced conductive elements in alineararray along the slot extend between this wall surface and aconductive base member positionedopp'osite thereto, successive elementsof the linear 2,746,036 Patented May 15, 1956 array being connected onopposite sides of the slot in the wall surface. Then, the electronstream to be coupled is projected contiguous to and along the lineararray. The separations and lengths of the conductive elements and theaverage velocity of the electron stream are adjusted to secureinteraction between the electron stream and the ields associated withthe conductive elements'.

In a specific illustrative embodiment for coupling an electron s'trea'mto a transverse electric wave traveling in a rectangular wave guide, oneof the narrow side walls of the wave guide is slotted parallel to thedirection of wave propagation, and successive wire elmen'ts eachapproximately a half Wave-length long extend across the electron stream,spaced apart therealong approximately half an electronic wavelength.Electronic wavelength is the distance between corresponding phases oftwo consecut'ive cycles of a space charge wave in an electron stream.Or, electronic wavelength is the distance trav-y eled by an electronduring one cycle of the signal. i The invention will be betterunderstood from the following more detailed description taken inconnection with the accompanying drawings in which: Fig. 1 shows inperspective a basic coupling arrangement of the invention; p h

Figs. 2A and 2B are side and sectional views, respectively, of a numberof adjacent wire elements `rof the arrangement of Fig. 1 forillustrating the directions of electric fields and currents associatedtherewith; y K Figs. 3A and 3B shows a microwave amplifier in? whichthere are incorporated as the input and outputdsignal transducersmodiiications of the basic arrangement of Fig. 1; and l Fig. 4 shows adirective antenna array which also in# corporates a form of thearrangement kof Fig.- 1. 4

With more specific reference now to the drawings, ig'. l showsschematically a basic arrangement `fdr coiipling in accordance with theinvention. An electron stream 11, provided from some suitable source nothere shown, is` projected along a linear array of wire elements 12 whichextend between two oppositelyr disposed conductive members, a basemember 13 which can, for example, be a portion of the envelope enclosingthe electron stream and a wall member 14, which'can', for example, be awall of a' wave guide, cavity resonator, antenna or some otherconductively bounded wave guiding element, above which exist, or are tobe induced electromagnetic waves characterized by wavelengths long withrelation to the corresponding electronic wavelengths. In the case t belirst described, it will be assumed thattlie signal waves associatedwith the wall member are to be impressed as signal modulations of theelectron stream. Sbsequeiitly, the converse case is to be brieydescribed in which signal modulations on the electron stream are made'to set up electromagnetic Waves for propagation above the wall member14. This wall membery is apertured tdform the slot 15 which extendsparallel to the electron flow. The orientation of the electron flow andthe wally member is chosen originally so that the slot 15 will extendtransverse to the current flow induced in the wall 14 by theelectromagnetic waves associatedl therewith. Successive wire elements 12extend normal to the direction of electron How from opposite sides ofthe slot` 15 to the base member 13, forming a linear array whichproceeds rin the direction of the electron strean. The length of thewires is chosen so that most ofy the current which formerly Went acrossthe slot will now proceed from one side of the slot down one set ofalternate wires and up the other set of alternate wires to reappear onthe'lop'- psite side of the slot in approximately the same phase aswould be the case if the slot had not beenV cut, If this condition lismet, the fields above the wall will4 not: be appreciably disturbed bythe presence of the slot. It can I seen that to satisfy this condition,the extra distance through which the current passes should beapproximately an integral number of wavelengths. For wire elements ofuniform length, this means that each wire is to be approximately anintegral number of half wire wavelengths long. The wavelength along thewire elefments is determined principally by the wire diameter and[spacing and generally'will be approximately the free v -fields betweenadjacent wire elements and the currents 'along the wire elements whenthe wire lengths satisfy thel above-described condition. As is shown,the current flow I'is in opposite directions along adjacent wire ele-"ments 12 and accordingly, the electric yfield E reverses betweenadjacent elements. As is indicated vectorially, the electricfieldsbetween wire elements vary alongthe lengths of the wire elements, beingka maxima at the centers and a minima at the ends. As is well known in'the microwave art, for useful interaction between the electron kstreamand the electric fields set up by the signal -waves (i.'e., foramplification of the waves on the electron stream), the changes indirectiony of the electric fields should reinforce the bunching effectin the electron stream. In the present case since the electric fieldreverses direction between successive elements, for synchronism thecenter-to-center spacing between successive wire elements shouldcorrespond approximately to an integral odd number of electronic halfwavelengths where the electronic wavelength is the free space wavelengthof the signal excitation multiplied by the ratio of the average velocityof the electron stream to the velocity of light. Generally it isadvantageous to adjust the electron velocity so that thecenter-to-center wire spacing is approximately one half an electronicwavelength. When the various conditions specified are sufficiently wellsatisfied, signal waves which induce iiow in the wall member '.14 areimpressed on the electron stream 11 asl waves which travel therealong.

It is also accordance with the invention to utilize this same structureto abstract power from an electron stream on which are traveling signalmodulations. In this case, the signal modulations on the electron stream11 induce 'currents in the linear array of wire elements 12 whichcirculate currents in the wall member 14 which set up waves above thewall member which correspond to the signal modulations.

Various other factors are to be considered in arriving atthe particularconfiguration of the coupling arrangement which is most advantageous fora specific application. To intercept the maximum current fiow induced inthe ywall member 14, the s lot 15 should extend perpendicular'to thedirection of this current flow. The choice of exact location ofthe slotin the wall member is influenced by impedance matching considerations,various locations generally affording different impedance matchesbetween the linear array and the slotted Wall member. lf the width ofthe slot is too narrow, the capacitance across the slot tends to shortout the array of wire elements with a consequent loss in efiiciency. `If4too wide a slot is provided, the radiation losses become excessive. Thelength of the slot and the number of wires in fthe array must also beadjusted to provide adequate energy transfers between the electronlstream and 'the signal waves. y

` The choice of wire size is also goverened by various 4 factors. Thehner the wire the greater the problems of fabrication, the less sturdythe structure, and the lower the power handling capacity. Moreover, fora given range of accelerating electron voltages, the larger the wire thecloser the spacing if the center-to-center wire spacing is to beapproximately half an electronic wavelength. However, since too closewire spacing results in too low a linear array impedance, upperlimitations on the size of wire then exist. It is of course notnecessary that the wire elements be circular in cross section, Isinceribbon-type or other forms can also be utilized.` However, the readyavailability of wire of circular cross section together with presentlyknown grid winding techniques makes use of such wire generallyadvantageous.

The basic arrangement just described can conveniently be modified forincorporation in various microwave devices in whichinput wave signalsare madeto excite modulations in an electron stream which are thereafteramplified as they proceed along the stream to be thereafter employed toinduce amplified waves into an output circuit. Figs. 3A and 3B areperspective and sectional views, respectively of a microwave amplifierwhich is particularly well suited for incorporating input and outputtransducers of the kind jus-t described. Within an evacuated elongatedtubular envelope 20, which, for example, can be of a non-magnetic metalsuch as copper, at opposite ends an electron gun 21 and a targetelectrode 22 define a path of electron flow. The electron gun can be ofconventional structure including an electron emissive cathode surface21A, a heater unit 21B, intensity control lelements 21C, and variouselectrodes for collimating and accelerating the stream, which have beenshown here schematically as the apertured plate 21D for the sake ofsimplicity. It is usually desirable to employ magnetic flux producingmeans (not shown here) external to the envelope to provide alongitudinal magnetic lfel'd to minimize transverse components ofelectron flow. Upstream along the ow, input waves are impressed assignal :modulations on ithe electron stream by an input transducer `23in accordance with the invention. In this embodiment, input transverseelectric waves are applied byk way of a rectangular wave guide 24, whichfor example, is a continuation by way of the pressure tight glass window25 of a wave guide transmission system. The orientation of the variouscomponents is such that the narrow side wall 26 of the wave guide iscontiguous or integral with the top surface of the tube envelope 20 andthat the direction of wave propagation is in the direetion of electronflow. With such an orientation, the side wall 26 serves conveniently therole of the wall member 14 referred to in the description of the basicarrangelment of Fig. 1. The wall 26 is then apertured to form the slot27 extending in the direction of electron ow which also corresponds to adirection transverse to the current fiow induced in the wall 26 bytransverse electric waves inthe wave guide 24. Then spaced wire elements"28 are connected in a linear array along the path of electron flow fromthe wall surface 26 to the opposite surface 26A of the Vtube envelope,which in this way -serves las the base member 13 referred -to inthearrangement of Fig. 1. As in that arrangement, successive elements 28 ofthe linear array extend from opposite sides of the slot 27 to the base26A. Moreover, it is advantageous that the successive elements be spacedapart approximately half an electronic wavelength, which relationship ismost conveniently realized by an appropriate choice of velocity ofelectron flow after a convenient wire spacing has been chosen. Moreover,each wire element 28 should advantageously be approximately half asignal wavelength long, which relationship fixes the separation be'tweenthe slotted wall 26 andthe base surface 26A. The slot 27 is made ofsufficient length so that the input waves applied to the wave guide 24effect adequate modulationl of the electron stream.

Since the electric field associated with the linear array of wireelements is generally strongest between the central portions thereof,falling olf between thel ends, it is advantageous toconiine the electronflow to these central portions. To secure the maximum coupling and hencemaximum elect, the stream should ow past the wire elements as closely aspossible.

For the amplication of the impressed modulations, the amplifier shownemploys as the amplifying means a linear array of resonant wire elements28A similar to those employed in the input transducer 23 and past whichthe electronstream continues. These wire elements 28A, eachapproximately half a signal wavelength long, are also connected acrossthe tube envelope, spaced apart along the direction of iiowapproximately half an electron stream wavelength. Asl is described inthe copending application of J. R. Pierce, Serial No. 150,429, filedMarch 18, 1950, now Patent No. 2,708,236, dated May 10, 1955,ampliiication of the signal modulations on the electron stream isobtained from the interaction between the electron stream and theelectromagnetic elds associated with these wire resonators. Beyond thisamplilier section, energy is abstracted from the signal modulations onthe stream by an output transducer 33 which resembles the inputtransducer 23. In this case, one of the narrow side walls of the outputwave guide 34 serves as the wall member 36 which is apertured to formthe slot' 37. Then as before, wire elements 38, in a linear array, areconnected across the tube envelope, successive elements extending fromopposite sides of the slot 37 to the opposite surface of the tubeenvelope. By means of this output transducer, ampliied output Waves areset up in the wave guide 34 which can be a further continuation by wayof a pressure tight glass window 35 of a wave transmission system.

It can be seen that various congurations are possible for input andoutput transducers for incorporation in an amplilier of the kinddescribed. For example, the orientation of the input wave guide 24 canbe rotated 90 degrees clockwise such that the end surface 29 becomescontiguous with the tube envelope for use as the slotted wall member. Inthis case, the slot is made to extend along the broad dimension of thisend wall. As is known in the art, such a slot would intercept thecurrent ow induced in the end wall by transverse electric Waves beingreected by this end wall, and accordingly, such a configuration ispossible for the practice of the invention.

The basic coupling arrangement shown in Fig. 1 can be further adaptedfor use as a directional antenna array, as shown in Fig. 4, for energytransfers between space charge waves on electron streams and wavesradiating in free space. In this modiiication, as before, an electronsource and a collector electrode (not shown) define a path of electronow 41 along which are` spaced wire elements 42 in a linear array.Successive elements are connected from a common conductive base member43 alternately to one of the two conductive strips 44 and 45 whichextend along the array. It is generally convenient to obtain these twostrips by slotting a single conductive member 46, as shown here and asis characteristic of the basic arrangement of Fig. 1. Then, if thedimensions and spacing of the wire elements 42 is as described earlier,signal waves on the electron stream will induce oppositely directedcurrents in successive Wire elements Which will combine in the member 46to set up a transverse current flow thereacross. Now by suitablypositioning a conductive. plate member 47, apertured for forming asuccession of radiating slots 48, parallel to the member 46, thereresults an antenna which can be made directive by appropriate spacing ofthe slots 48 in the manner known in the antenna art.

An--oscillator which incorporates aV transducer arrangementof the kinddescribed forms the basis of the copend- 6 ing application, SerialNo;278,323 tiled March-25, 1952, by D. W. Hagelbarger and L. R. Walker.

Itis to be understood that the above-described arrangements are merelyillustrative of the principles of the invention. Various otherembodiments can be' devised by a worker skilled in the art withoutdeparting from the spirit and scope of the invention.

What is claimed is:

1. In microwave apparatus, a base member, a wave transmission memberhaving a wall surface positioned opposite said base member and aperturedto form a slot transverse to the current liow induced therein by wavespropagating along said member, a linear array of spaced wire elementseach having a length approximately an integral number of halfwavelengths of said waves, successive elements extending from oppositesides of the slot in the wall to said base member, and means for formingand projecting a charge stream past said wire elements in the directionof extent of the linear array.

2. In microwave apparatus, means forming and projecting a charge stream,a conductive base member and a conductive wave transmission wall memberon opposite sides of the electron stream, the wall member apertured toform a slot extending in the direction of the elec'- tron stream andtransverse to the direction of the current iiow induced in the wallmember by waves propagating therealong, and a linear array of spacedconductive elements each having a length approximately an integralnumber of half wavelengths of said waves, successive elements extendingfrom opposite sides of said slot in said wall member to said base memberin field coupling rela-.

tion with said electron stream.

3. In microwave apparatus, means forming and projecting an electronstream, a conductively bounded wave guiding member having a wall surfaceapertured to form a slot extending in the direction of the electronstream and transverse to the current flow induced in the wall member bywaves propagating therealong, a conductive base member positionedopposite said apertured wallsurface, and a linear array of spaced wireelements each having a length approximately an integral number of halfwavelengths of said waves, successive elements extending from oppositesides of said slot in said wall surface to said base member in fieldcoupling relation with said electron stream.

4. In microwave apparatus, a conductive base member, a conductive wavetransmisison wall member positioned opposite said base member andapertured to form a slot extending in a direction transverse to thecurrent flow induced in the wall member by waves propagating therealong,a linear array of spaced conductive elements, each approximately anintegral number of half wavelengths long, successive elements extendingfrom opposite sides of the slot in the wall member to said base member,and means for forming and projecting an electron stream in tieldcoupling relation along the linear array of conductive elements.

5. In microwave apparatus, means forming and projecting an electronstream, a conductive base member anda conductive wave transmission wallmember on opposite sides of the electron stream, the wall memberapertured to form a slot which extends in the direction of the electronstream and transverse to the current ilow induced in the wall member bywaves propagating therealong,*` and a linear array of spaced conductiveelements, each approximately an integral number of half wavelengthslong,.successive elements extending: from opposite sides ofthe slot in saidwall member to said base member in iield coupling relation with theelectron stream and spacedy apart along said stream approximately an oddnumber of half electronic wavelengths.

6. In microwave apparatus, means forming and projecting an electronstream, a conductivel base-member anda conductive wave transmissionwalll member on opposite sides of the electron stream, the wall memberapertured to form a slot along the direction of electron flow andtransverse to the direction of current flow induced in the Wall memberby waves propagating therealong, and a linear array of spaced wireelements, each approximately half a wavelength long, successiveelementsy extending from opposite sides of the slot in the wall memberto the base member in field coupling relation with the electron streamand spaced apart therealong approximately half an electronic wavelength.

7. In microwave apparatus, a conductively bounded wave transmissionmember having a wall surface apertured to form a slot transverse to thecurrent iiow induced inV said wall surface by Waves propagating therein,a conductive base member positioned opposite said apertured surface,means for forming and projecting an electron stream along a pathparallel to said slot intermediate between said base member and saidapertured wall surface, and a linear array of spaced conductiveelements, each approximately half a wavelength long, successive elementsextending from opposite sides of the slot in the wall surface to thebase member in field coupling relation with the electron stream andspaced apart therealong half an electronic wavelength. Y v 8. In amicrowave tube, an electron source and target electrode defining a pathof electron flow, and transducer means, in an energy exchangerelationship with said flow, comprising a conductively bounded waveguiding memyber slotted in one'boundary surface along the direction ofelectron fiow and transverse to the current fiow induced in said waveguiding member by waves propagated there- 'along, a base conductivemember separated from said slotted boundary surface by the path ofelectron fow, and a linear array of spaced conductive elements eachapproximately an integral number of half wavelengths along, successiveelements extending from opposite sides of the slot in said boundarysurface to said base member in field coupling relation with saidelectron ow.

9. In a microwave tube, an electron source and a target electrodedefining a path of electron ow, and transducer means, in energy exchangerelation with the electron flow, comprising a conductively bounded Wavetransmission member having a boundary surface apertured to form a slottransverse to the current ow induced in said boundary surface by wavesin said member, the transmission member being disposed so that the slotextends in the direction of electron fiow, a conductive base memberpositioned opposite the apertured boundary surface, and a linear arrayof spaced conductive elements each element approximately an integralnumber of half wavelengths long,'successive elements extending fromopposite sides of the slot in said boundary surface to said base memberinfield coupling relation with the electron flow.

l0. In a microwave tube, an electron source and a target electrodedefining a path of electron flow, and transducer means, in energyexchange relation with the electron flow, comprising a conductivelybounded wave transmission member having a boundary surface apertured toform a slot transverse to the current flow induced in said boundarysurface by waves in said member, Said member being disposed so that theslot extends in the direction of electron flow, a conductive base memberpositioned opposite the apertured boundary surface, and a linear arrayof spaced conductive elements,each approximately half a wavelength long,successive elements extending from opposite sides of the slot in saidboundary surface to the base member and spaced apart along the path ofelectron flow approximately half an electronic wavelength.

l1. In a microwave tube, a conductive envelope, an electron source andtarget electrode defining a path of electron flow within said envelope,and transducer means in energy exchange relation with the electron flowcomprising a conductively bounded Wave guiding member having oneboundary surface contiguous to said conductive envelope and apertured toform a slot extending in the direction of electron ow and transverse tothe direction of current fiow induced in said boundary surface by wavespropagating therealong, and alinear array of spaced conductive elements,each approximately an integral num-` ber of half wavelengths long,successive elements'extending from opposite sides of the slot in saidapertured boundary surface to the opposite side of the conductiveenvelope in field coupling relation with the electron flow.

l2. In a microwave tube, a conductive envelope, an electron source andtarget electrode defining a path of electron fiow within said envelope,and transducer means in energy exchange relation with the electron fiowcomprising a conductively bounded wave guiding member having oneboundary surface integral with said conductive envelope and slotted inthe direction of electron flow and transverse to the direction ofcurrent flow induced in said boundary surface by waves propagatingtherealong, and a linear array of spaced wire elements, eachapproximately half a wavelength long, successive elements cxtending fromopposite sides of the slot in said boundary surface to the oppositesurface of the conductive envelope in field coupling relation with theelectron ow and spaced apart along said path approximately a halfelectronic wavelength.

13. In a microwave device, a conductive envelope, an electron source andtarget electrode defining a path of electron flow within said envelope,and transducer means in energy exchange relation with the electron owcornprising a conductively bounded waveguide having one wall integralwith the conductive envelope and slotted in a direction transverse tothe current ow induced in said wall by waves in said wavcguidepsaidwaveguide being V disposed so that the slot extends in the direction ofelectron flow, land a linear array of spaced conductive elements, eachapproximately an integral number of half wavelengths long, successiveelements extending from said wall on opposite sides of the slot to theopposite wall of the conductive envelope in field coupling relation withthe electron fiow.

14.` A microwave device according to claim 13 in which the spacedconductive elements are wire elements spaced apart along the electronstream approximately half an electronic wavelength.

15. In a microwave device, an electron source and target electrodedefining a path for an electron stream, a plurality of spaced wireelements, each transverse to the path of the electron stream, in alinear array along said stream, input transducer means for impressinginput signals as modulations on said stream comprising a waveguidewhich-is supplied with input signals having a wall apertured to form aslot transverse to the current ow induced in said wall by input signalssupplied to the waveguide and extending in the direction of electron ow,successive elements of an upstream portion of said linear array beingconnected to opposite sides of said slot, and output transducer meansfor deriving output waves from signal modulations on said streamcomprising an output waveguide having a wall apertured to form a slotextendingalong the direction of electron ow, successive elements of adownstream portion of said linear array being connected to oppositesides of said last-mentioned slot.

l 16. In a microwave device, a conductive base member, a slottedwaveguiding member positioned opposite said base member, means formingand projecting an electron stream intermediate said base and waveguidingmember, the slot in said waveguiding member being parallel to thedirection of flow of the electron stream and transverse to the directionof current flow induced in the waveguiding member by waves propagatingtherealong, a linear array of wire elements each approximately anintegral number of half wavelengths long extending between said base andwaveguiding members in coupling relation with the electron stream,successive wire elements being connected to said waveguiding member onopposite sides of the slot therein, and an apertured conductive platepositioned opposite said waveguiding member on the side remote from saidbase member.

17. In a microwave device, an apertured conductive plate, a slottedconductive wave transmission plate with the slot transverse to thedirection of current How induced in the plate by waves propagatingtherealong, and a conductive base member positioned parallel to oneanother in the order named, a linear array of wire elements eachapproximately an integral number of half wavelengths long extendingbetween said slotted conductive plate and conductive base member,successive elements being connected to said slotted conductive plate onopposite sides of the slot therein, and means for forming and projectingan electron stream intermediate said slotted conductive plate andconductive base member along the linear array of wire elements.

18. A microwave device according to claim 13 in which the spacedconductive elements are spaced apart along the electron streamapproximately half an electronic wavelength, where the electronicwavelength is the free space 20 wavelength of the signal excitationmultiplied by the ratio of the average velocity of the electron streamto the velocity of light.

References Cited in the le of this patent UNITED STATES PATENTS OTHERREFERENCES Millman: A Spatial Harmonic Traveling Wave Amplier etc. Proc.I. R. E. for September 1951 (vol. 39 No. 9), pages 1035-1043, photo in179-171-18.

Pierce: Traveling Wave Tubes, copyright 1950, pages 85 to 92. (Copy inDivision 70.)

